Firm starter

or 4 hours since the 4th refreshment?  If the former, the yeast and bacteria are now very diluted and will take quite a while (maybe a day or so) to bounce back.  If the latter, just wait.  It will be ready when it's ready.

There appear to be some small bubbles in the dough.  There is also some moisture condensing on the inside of the jar.  Both of those are signs of life and activity by the yeasts and bacteria.  What is the temperature in your kitchen?

There are two lessons that we all learn when working with yeasted doughs.  The first is "Watch the dough, not the clock."  The second is "If the secret of baking is patience, the secret of sourdough baking is even more patience."  In your starter's case, what you want to learn is how long it takes to peak, not how long it takes to double.  That may take several more hours.  And the maximum expansion might be triple or even quadruple the original volume before it begins to slowly collapse.  Once you have that information, you can begin to adjust your feeding schedules and ratios to favor the faster-growing yeasts in your starter.  Please note that "faster" is a relative term.  You may be able to condition your starter to peak in 4-6 hours instead of 8-12 hours, assuming temperatures in the mid-70F range or warmer.

For now, keep an eye on it.  Record the time to peak expansion.  Measure that volume relative to the original volume.  Feed it again.  Repeat the measuring and noting.  After a few cycles, you'll have a very good idea of how your starter behaves in the current conditions.

Paul

I see a little lift I'd let it sit